If `|x|<1,` then the coefficient of `x^n` in expansion of `(1+x+x^2+x^3+)^2` is a. `n` b. `n-1` c. `n+2` d. `n+1`

If f(x) = |(x + lamda,x,x),(x,x + lamda,x),(x,x,x + lamda)|, " then " f(3x) - f(x) =

If f(x) = |(1,x,x+1),(2x,x(x-1),x(x+1)),(3x(x-1),x(x-1)(x-2),x(x+1)(x-1))| , using properties of determinant, find f(2x) - f(x).

If x is a negative integer, then (a) x+|x|=0 (b) x-|x|=0 x+|x|=-2x (d) x=-|x|

If x is a positive integer, then (a) x+|x|=0 (b) x-|x|=0 (c) x+|x|=-2x (d) x=-1|x|

If x is a negative integer, then (a) x+|x|=0 (b) x-|x|=0 (c) x+|x|=-2x (d) x=-|x|

If f(x)=sgn(x)={(|x|)/x,x!=0, 0, x=0 and g(x)=f(f(x)), then at x=0,g(x) is

If {x} and [x] represent fractional and integral part of x respectively then solve the equation x-1=(x-[x])(x-{x})

Solve the following : (i) |x-2|=(x-2) " (ii) " |x+3| = -x-3 (iii) |x^(2)-x|=x^(2)-x " (iv) " |x^(2)-x-2| =2+x-x^(2)

If f(x)=|[x-2, (x-1)^2, x^3] , [(x-1), x^2, (x+1)^3] , [x,(x+1)^2, (x+2)^3]| then coefficient of x in f(x) is

If f(x)= |1 x x+1 2x x(x-1)(x+1)x3x(x-1)x(x-1)(x-2)(x+1)x(x-1)| then f(500) is equal to a. 0 b. 1 c. 500 d. -500